Taxis operate essentially no differently than anywhere else. There are drivers with a “Taxi” sign on or in their car, and taxis that can be hailed via apps. All taxis are generally safe, but using a phone app is a more practical option since it prevents taxi drivers from overcharging, which is a prevalent problem especially if you don’t know Georgian or Russian. This is further exasperated by nearly all drivers not having and/or not using a meter to track the ride. Taxi trips within the city center shouldn’t cost much more than 15 GEL, and should typically cost less.
If arriving in Georgia via Shota Rustaveli Tbilisi International Airport, upon exiting the airport you will be greeted by numerous taxi drivers. These drivers nearly always charge a 50 GEL fare, which is a complete rip-off. A taxi from Tbilisi International Airport to the city center (up to about Medical University on Vazha-Pshavela Ave.) should not cost more than 30 GEL, especially at night when traffic outside of the airport is practically nonexistent.
The most common taxi apps in Georgia are Bolt (formerly Taxify) and Yandex.Taxi (Uber does not operate here). For whatever reason, the drivers for these apps will often ask where you are going once you enter the vehicle, and may even ask you to explain where it is if they do not know of it, rather than simply using their phones as one might expect from an Uber driver.